Global existence and large time behavior of classical solutions to the two-dimensional micropolar equations with large initial data and vacuum

This paper concerns the global existence and large time behavior of classical, strong, and weak solutions to the two-dimensional compressible micropolar equations with large initial data and vacuum. We assume that the shear and angular viscosity coefficients are positive constants and the bulk coefficient is lambda=rho beta, where rho is the density and beta > 3/2. It is crucial to derive an upper bound of the density uniformly in the time such that all the classical, strong, and weak solutions converge to the equilibrium state as the time tends to infinity.

Automated summary

This paper discusses the global existence and long-time behavior of classical, strong, and weak solutions to the two-dimensional compressible micropolar equations with large initial data and vacuum. The key is to derive an upper bound of the density uniformly in time to ensure that all solutions converge to equilibrium state as time tends to infinity.